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Regularization Of Cauchy Problem For 2d Time-Fractional Diffusion Evolution Equations

Author

Listed:
  • TRAN THANH BINH

    (Faculty of Mathematics and Applications, Sai Gon University, Vietnam)

  • NGUYEN PHUC BINH

    (Faculty of Mathematics and Applications, Sai Gon University, Vietnam)

  • BUI DINH THANG

    (Faculty of Mathematics and Applications, Sai Gon University, Vietnam)

  • LE DINH LONG

    (Division of Applied Mathematics, Science and Technology Advanced Institute, Van Lang University, Ho Chi Minh City, Vietnam3Faculty of Technology, Van Lang University, Ho Chi Minh City, Vietnam)

Abstract

In this work, we focus on an initial value problem for a class of 2D time-fractional diffusion evolution equations with Riemann–Liouville fractional derivative. There are three new results in this paper. First of all, the existence and ill-posedness result (in the sense of Hadamard) in three cases which are consisting of homogeneous, inhomogeneous, and nonlinear problems are considered. Next, by using the Fourier truncation method, we show that regularized problems are well-posed. Finally, some demonstrated examples are presented to test the proposed method.

Suggested Citation

  • Tran Thanh Binh & Nguyen Phuc Binh & Bui Dinh Thang & Le Dinh Long, 2022. "Regularization Of Cauchy Problem For 2d Time-Fractional Diffusion Evolution Equations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(05), pages 1-25, August.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:05:n:s0218348x22401818
    DOI: 10.1142/S0218348X22401818
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